| Indicator ID | NA |
| Indicator Name | My Great Indicator |
| Country | NA |
| Continent | NA |
| Ecosystem Condition Typology Class | NA |
| Realm | NA |
| Biome | NA |
| Ecosystem | NA |
| Year added | 1901 |
| Last update | NA |
| status | incomplete |
| Version | 000.001 |
| Version comment | NA |
| url | https://github.com/NINAnor/ecRxiv |
Pollinator Indicators
Pollinator indicators
1. Introduction
We aim to model the diversity of pollinators in Norway given their know interaction with some plant species. From the estimated diversity across the nation, we intend to look at the estimates in the ASO Data meadows by using their values as the reference values. To achieve this, we do the following:
obtain data from GBIF for bumblebees, butterflies and bees
fit an integrated species distribution model (ISDM) to the data to obtain pollinator intensities
obtain a web plot of the pollinator and plant species
get data on the interaction plant species from GBIF
fit an ISDM to the plant species data to obtain the species occurrence probability
estimate the alpha diversity index of the pollinators across Norway
2. About the underlying data
The pollinator and plant species data used to fit the ISDMs were obtained from GBIF. Cite the DOI of the downloaded data.
2.1 Spatial and temporal resolution
Both pollinator and plant data obtained was for the entire Norway observed within \(2005\) to \(2024\). For each dataset within the downloaded GBIF data, we formatted them based on their meta data into presence-only and presence-absence data. Then, we merge all the presence-absence datasets into one dataset: mergedDatasetPA and all the presence-only datasets into one dataset: mergedDatasetPO. The number of occurrences in each dataset for the pollinators are presented in Table 2.
| Dataset | Pollinator | No. of observations |
|---|---|---|
| Presence-only | Bees | 84485 |
| Butterflies | 474857 | |
| Hoverflies | 79683 | |
| TOTAL | 639025 | |
| Presence-absebce | Bees | 40429 |
| Butterflies | 39321 | |
| Hoverflies | 51861 | |
| TOTAL | 131611 |
| Plant species | Presence-absence | Presence-only |
|---|---|---|
| Ajuga pyramidalis | 72650 | 4427 |
| Astragalus alpinus | 155978 | 2283 |
| Campanula rotundifolia | 218345 | 13558 |
| Carum carvi | 47681 | 2962 |
| Filipendula ulmaria | 163248 | 18103 |
| Galium album | 65106 | 3734 |
| Galium aparine | 45202 | 1926 |
| Galium boreale | 67332 | 8338 |
| Galium elongatum | 43791 | 1503 |
| Galium palustre | 84951 | 2598 |
| Galium saxatile | 5048 | 1619 |
| Galium uliginosum | 49728 | 2061 |
| Galium verum | 23600 | 3619 |
| Geranium robertianum | 49141 | 6148 |
| Geranium sylvaticum | 238108 | 15692 |
| Gymnadenia conopsea | 458 | 3659 |
| Hieracium murorum | 764 | 30 |
| Hieracium umbellatum | 9808 | 3985 |
| Hieracium vulgatum | 13483 | 39 |
| Hypochaeris radicata | 1988 | 1399 |
| Knautia arvensis | 50898 | 6609 |
| Lathyrus linifolius | 91357 | 6438 |
| Lathyrus pratensis | 77899 | 5923 |
| Lathyrus vernus | 56287 | 2228 |
| Leucanthemum vulgare | 125584 | 9992 |
| Lotus corniculatus | 64438 | 12485 |
| Nardus stricta | 47131 | 7179 |
| Origanum vulgare | 767 | 2484 |
| Plantago lanceolata | 8672 | 5638 |
| Plantago major | 6730 | 7200 |
| Plantago media | 1389 | 2442 |
| Silene dioica | 56046 | 7645 |
| Silene vulgaris | 33839 | 3742 |
| Stellaria graminea | 180580 | 8687 |
| Stellaria media | 47587 | 4101 |
| Stellaria nemorum | 62024 | 4250 |
| Trifolium medium | 35383 | 4670 |
| Trifolium pratense | 147575 | 12698 |
| Trifolium repens | 97671 | 11745 |
| Trollius europaeus | 44249 | 5928 |
| Valeriana sambucifolia | 68074 | 108 |
| Veronica alpina | 17738 | 626 |
| Veronica chamaedrys | 175299 | 9228 |
| Veronica officinalis | 223994 | 11936 |
| Veronica serpyllifolia | 5988 | 3153 |
| Vicia cracca | 83519 | 10301 |
| Vicia sepium | 112154 | 6270 |
| Vicia sylvatica | 45135 | 2214 |
| Viola biflora | 3518 | 3612 |
| Viola canina | 123557 | 3602 |
| Viola epipsila | 611 | 499 |
| Viola palustris | 83363 | 8928 |
| Viola riviniana | 425049 | 9602 |
| Viola tricolor | 88517 | 4075 |
Iintend to keep either the table or the figures in the final document, depending on what is needed for the report.
2.2 Original units
2.3 Additional comments about the dataset
3. Indicator properties
3.1. ECT
3.2. Ecosystem condition characteristic
3.3. Other standards
3.4. Collinearities with other indicators
4. Reference condition and values
4. 1. Reference condition
4. 2. Reference values
4.2.1 Minimum and maximum values
Reference values for diversity indices at the ASO data meadows.
ggplot(asoDataMeadows) +
gg(asoDataMeadows["overallDiversity"], aes(col = overallDiversity)) +
scale_fill_gradientn(colours = terrain.colors(30))#+
#geom_sf(data = regionGeometry, alpha = 0.1)4.2.2. Threshold value for defining good ecological condition (if relevant)
4.2.3. Spatial resolution and validity
5. Uncertainties
6. References
7. Datasets
7.1 Dataset A
7.2. Dataset B
7.3. Covariates
Write a summary of the covariate names and how they were obtained in a table. Have an Yes / No indicating whether they were used to fit pollinator or plant ISDM.
The environmental covariates used for the model is presented in Figure 3.
8. Spatial units
9. Analyses
We fitted an ISDM using the point process framework [REF] to the merged pollinator presence-only (PO) and presence-absence (PA) datasets. ISDMs are various models that are linked together by a shared ecological process.
Using the poisson process framework, we model the presence-only data as a Poisson point process model [REF] with mean intensity \(\lambda_i(s)\) for each pollinator \(i \in \{bees, butterflies, hoverflies\}\). This mean intensity is modelled as: \[\begin{equation} \label{eq:int} \ln(\lambda_i(s)) = \beta_{0i} + \beta_{ji} X_j(s) + \omega_i(s) + \eta(s), \end{equation}\] where \(\beta_{0i}\) is the pollinator-specific intercept, \(\beta_{ji}\) is the pollinator-specific effect of covariate \(j\), \(X_j(s)\) is the \(j^{th}\) covariate field, \(\omega_i(s)\) is the pollinator-specific spatial autocorrelation field and \(\eta(s)\) is the bias field. \(\omega_i(s)\) and \(\eta(s)\) are modeled as zero mean Gaussian random field (i.e. \(\omega_i(s) \sim N(0, \Sigma)\), where \(\Sigma\) is a Mat’ern covariance matrix with variance \(\sigma_{\omega}^2\) and range \(\kappa\) and \(\eta(s) \sim N(0, \Sigma_\eta)\), where \(\Sigma_\eta\) is a Mat’ern covariance matrix with variance \(\sigma_{\eta}^2\) and range \(\kappa_\eta\)).
We model the PA with a logistic regression model. Let \(y_i(s)\) be a binary value at location \(s\) with \(0\) indicating absence of pollinator \(i\) and \(1\) indicating presence of pollinator \(i\). Then \(y_i(s) \sim \text{Bernoulli}(\Psi_i(s))\) with: \[ cloglog(\Psi_i(s)) = \beta_{0i} + \beta_{ji} X_j(s) + \omega_i(s) \] where the parameters are defined in equation \(\ref{eq:int}\).
All the ISDMs were fitted using the R-package PointedSDMs [REF].
9.1. ISDM for pollinators
Using the model framework defined above, we fitted the ISDM to the pollinator dataset obtained from GBIF.
model <- PointedSDMs::startSpecies(PointsBeesAndButterfliesAndHoverflies, # list of pollinator dataset (containing both mergedDatasetPA and mergedDatasetPO)
Boundary = regionGeometry, # boundary of the study
Projection = newCrs, # projection
Mesh = meshForProject, #mesh used for the model
speciesEnvironment = TRUE, # Should we have pollinator specific covariate effect
speciesIntercept = TRUE, # TRUE treats the intercept as a random effect, instead of constrained as with a fixed effect
pointsIntercept = FALSE, #should we include intercept for each dataset
pointCovariates = FALSE, #do we have covariates for the presence-only data
responsePA = 'individualCount', # column name of the response values for presence-absence data
# trialsPA = 'trials',
spatialCovariates = envCovsForModel, # raster of spatia covariates
speciesName = 'Taxon', # Names of the species in the datasets
pointsSpatial = NULL, # Do not include a dataset spatial field
speciesSpatial = "replicate") # unique spatial field per species, but they share the same hyperparameters.
# Add second bias field for PO data
model$addBias(datasetNames = 'mergedDatasetPO')Priors
We assume the following priors for the pollinator ISDM:
The probability that the standard deviation of the pollinator spatial field is greater than \(0.1\) is \(0.1\) (i.e. \(P(\sigma_\omega > 0.1) = 0.1\)).
The probability that the standard deviation of the bias field is greater than \(0.1\) is \(0.1\) (i.e. \(P(\sigma_\eta > 0.1) = 0.1\))
The probability that the spatial range of the pollinator spatial field is greater than \(50\) is \(0.1\) (i.e \(P(\kappa_\omega < 50) = 0.1\))
The probability that the spatial range of the pollinator spatial field is greater than \(50\) is \(0.1\) (i.e. \(P(\kappa_\eta < 50) = 0.1\))
# hyper parameters of the spatial field (shared across species)
model$specifySpatial(Species = TRUE, # define same prior for the all species
prior.sigma = c(0.6, 0.1), # SD of field variation;
prior.range = c(5, 0.1)) # range of spatial correlation;
model$specifySpatial(Bias = TRUE, # Change the prior
prior.sigma = c(1, 0.1),
prior.range = c(5, 0.1))
model$specifyRandom(
# precision parameter on how much each species' spatial field (how much they can deviate from the shared ___)
speciesGroup = list(model = "iid",
hyper = list(prec = list(prior = "pc.prec",
param = c(0.1, 0.1)))),
# precision parameter on the baseline species occurrence rate
speciesIntercepts = list(prior = 'pc.prec',
param = c(0.1, 0.1))) Fit model and make predictions
We fit the model and make predictions of the pollinator intensity within the study region.
modelRun <- PointedSDMs::fitISDM(data = model,
options = modelOptions)
# predictions for this model
individualDatasetPreds <- predict(modelRun,
data = ppxl,
predictor = TRUE,
n.samples = 100)9.2. ISDM for plant species
Modelling all the \(54\) species required memoey allocations we did not have, so we split the species into groups with \(10\) species in each group. We fitted independent ISDMs for each of the groups.
# PointedSDMs takes a longer time to fit for many species
# The trick to to break it into smaller groups
# The split will be done by the number of present speccies in each location
# I will split it nGroups time
sortedSpecies <- table(asoDatasf$acceptedScientificName)%>%
as.data.frame()%>%
dplyr::arrange(desc(Freq))%>%
select(Var1)%>%
c()
# Set the number of groups
nGroups <- 10
#split the species into groups of 10 species in each
plantSpeciesGroup <- split(sortedSpecies$Var1,
seq(1,
ceiling(length(sortedSpecies$Var1)/nGroups)))Similar to the model the pollinator ISDM, we fitted an ISDM to the \(54\) plant species. The ISDM has species-specific intercept, covariate effect and spatial field (but all the species share the same hyperparameters). We also added a spatial bias field to the observation model for the presence-only dataset.
speciesModelShared <- PointedSDMs::startSpecies(formatPlantData,
Boundary = regionGeometry,
Projection = newCrs,
Mesh = meshForProject,
responsePA = 'individualCount',
speciesEnvironment = TRUE,
speciesIntercept = TRUE,
spatialCovariates = envCovsForPlantSpeciesModel,
speciesName = 'simpleScientificName',
pointsIntercept = FALSE,
pointsSpatial = NULL, # Do not include a dataset spatial field
speciesSpatial = "replicate")
# Add bias spatial field for the PO dataset
speciesModelShared$addBias(datasetNames = 'mergedPlantsPO')Priors We assume the following priors for the pollinator ISDM:
The probability that the standard deviation of the pollinator spatial field is greater than \(0.1\) is \(0.1\) (i.e. \(P(\sigma_\omega > 0.1) = 0.1\)).
The probability that the standard deviation of the bias field is greater than \(0.1\) is \(0.1\) (i.e. \(P(\sigma_\eta > 0.1) = 0.1\))
The probability that the spatial range of the pollinator spatial field is greater than \(50\) is \(0.1\) (i.e \(P(\kappa_\omega < 50) = 0.1\))
The probability that the spatial range of the pollinator spatial field is greater than \(50\) is \(0.1\) (i.e. \(P(\kappa_\eta < 50) = 0.1\))
# hyper parameters of the spatial field (shared across species)
speciesModelShared$specifySpatial(Species = TRUE, # define same prior for the all species
prior.sigma = c(1, 0.1),
prior.range = c(5, 0.1))
speciesModelShared$specifySpatial(Bias = TRUE, # Change the prior
prior.sigma = c(0.6, 0.1),
prior.range = c(5, 0.1))
# prior for random effects (mesh nodes of spatial field and species intercepts)
speciesModelShared$specifyRandom(
# precision parameter on how much each species' spatial field (how much they can deviate from the shared ___)
speciesGroup = list(model = "iid",
hyper = list(prec = list(prior = "pc.prec",
param = c(0.1, 0.1)))),
# precision parameter on the baseline species occurrence rate
speciesIntercepts = list(prior = 'pc.prec',
param = c(0.1, 0.1))) Model fitting and predictions
# specify the model options for INLA
modelOptions <- list(control.inla = list(int.strategy = 'eb',
diagonal = 0.1,
cmin = 0),
verbose = FALSE,
safe = TRUE)
# Species-specific spatial effects model
speciesSharedEst <- PointedSDMs::fitISDM(data = speciesModelShared,
options = modelOptions)
# I proceed with the prediction of occupancy probabilities
# over the entire region
individualDatasetPreds <- predict(speciesSharedEst,
data = ppxl,
predictor = TRUE,
n.samples = 10)9.3 Species Interractions
load("../data/webPlot.RData")
#interractionMatrix <- readr::read_csv(paste0(dataFolder,"/interractionsData/interractionMatrix.csv"))
bipartite::plotweb(WebReady[[1]])
9.4. Diversity Indices
To define the diversity of the pollinators, we estimate the pollinator intensity given their interaction with the plants species within the location \(s\). This is estimated as: \[\begin{equation} \begin{split} \text{Intensity for intensity} &\propto \text{Estimated pollinator intensity} \times \text{Interraction weight} \times \text{plant species occurrence probability}\\ \implies \lambda^{\star}_i(s) &= \frac{\lambda_i(s) \times w_{ik} \times \Psi_k(s)}{\sum_k \lambda_i(s) \times w_k \times \Psi_k(s)}, \end{split} \end{equation}\] where \(w_k\) is the weight of the interaction between pollinator \(i\) and plant species \(k\), \(\Psi_k(s)\) is the occurrence probability of plant species \(k\) and \(\lambda_i(s)\) is the intensity of pollinator \(i\).
We estimated the Hill’s diversity indices for the pollinators. The Hill’s diversity indices are defined as: \[ H(s) = r_i(s) \times log(r_i(s)); \] where \(r_i(s) = \frac{\lambda^{\star}_i(s)}{\sum_{i} \lambda^{\star}_i(s)}\).
10. Results
